# Nonlinear Optical Conductivity in Graphene and other 2-Band 2-D Materials

## TL;DR

This paper develops a quantum master equation framework to analyze the nonlinear optical conductivity of two-dimensional materials like graphene, silicene, and MoS2, highlighting their unique electronic responses to time-dependent electric fields.

## Contribution

It introduces a first-principles quantum master equation approach to study nonlinear optical responses in 2D Dirac materials, providing detailed analysis for graphene, silicene, and MoS2.

## Key findings

- Derived nonlinear optical conductivity expressions for graphene, silicene, and MoS2.
- Compared theoretical results with existing data, confirming the model's validity.
- Highlighted the impact of microscopic interactions on nonlinear responses.

## Abstract

Graphene, Silicene, $\mathrm{MoS}_2$ and other similar two-dimensional structures have unusual electronic properties that lend themselves to exotic device applications. These properties emanate from the fact that the electrons are endowed with Dirac fermion-like attributes. Thus these materials are not only characterized by certain fundamental principles, they also have amazing practical uses. Our emphasis here is on one such basic property concerning nonlinear response to time-dependent electric fields. We set up a first principle quantum master equation for the underlying density operator which is based on microscopic interactions between the Dirac electron with phonons and other electrons. While such an equation has general applicability to a variety of non-equilibrium phenomena in two-band systems, we focus onto the case of nonlinear optical conductivity. The derived results are separately analyzed for graphene, silicene and $\mathrm{MoS}_2$, and comparison made with other known results.